Class 11 Exam > Class 11 Questions > what is dimensional balance of an equation ho...
Start Learning for Free
what is dimensional balance of an equation how can we check the correctness of an equation by this
Most Upvoted Answer
what is dimensional balance of an equation how can we check the correc...
Dimensional Balance of an Equation:
Dimensional balance of an equation refers to the consistency of the dimensions of the physical quantities on both sides of the equation. In other words, it means that the units of measurement on the left-hand side of the equation are equal to the units of measurement on the right-hand side of the equation.
Checking the Correctness of an Equation Using Dimensional Balance:
Dimensional analysis is a powerful tool for checking the correctness of an equation. Here's a step-by-step process for checking the dimensional balance of an equation:
1. Identify the physical quantities involved in the equation.
2. Write down the dimensions of each physical quantity in terms of the fundamental units of measurement (such as meters, kilograms, and seconds).
3. Substitute the dimensions of each physical quantity into the equation.
4. Simplify the equation using algebraic rules.
5. Check that the dimensions on the left-hand side of the equation are equal to the dimensions on the right-hand side of the equation.
Example:
Let's consider the equation F = ma, where F is force, m is mass, and a is acceleration. To check the dimensional balance of this equation, we can follow these steps:
1. Identify the physical quantities involved: force, mass, and acceleration.
2. Write down the dimensions of each physical quantity: [F] = MLT^-2, [m] = M, [a] = LT^-2.
3. Substitute the dimensions into the equation: [MLT^-2] = [M][LT^-2].
4. Simplify the equation: [MLT^-2] = [MLT^-2].
5. Check that the dimensions on both sides of the equation are equal. Since they are, the equation is dimensionally balanced and therefore correct.
Importance of Dimensional Balance:
Dimensional balance is important because it ensures that an equation is physically meaningful. If an equation is not dimensionally balanced, it means that the units of measurement on one side of the equation do not match the units of measurement on the other side of the equation. This can lead to nonsensical or physically impossible results. By using dimensional analysis to check the dimensional balance of an equation, we can ensure that the equation is physically meaningful and can be used to make accurate predictions about the behavior of physical systems.
Dimensional balance of an equation refers to the consistency of the dimensions of the physical quantities on both sides of the equation. In other words, it means that the units of measurement on the left-hand side of the equation are equal to the units of measurement on the right-hand side of the equation.
Checking the Correctness of an Equation Using Dimensional Balance:
Dimensional analysis is a powerful tool for checking the correctness of an equation. Here's a step-by-step process for checking the dimensional balance of an equation:
1. Identify the physical quantities involved in the equation.
2. Write down the dimensions of each physical quantity in terms of the fundamental units of measurement (such as meters, kilograms, and seconds).
3. Substitute the dimensions of each physical quantity into the equation.
4. Simplify the equation using algebraic rules.
5. Check that the dimensions on the left-hand side of the equation are equal to the dimensions on the right-hand side of the equation.
Example:
Let's consider the equation F = ma, where F is force, m is mass, and a is acceleration. To check the dimensional balance of this equation, we can follow these steps:
1. Identify the physical quantities involved: force, mass, and acceleration.
2. Write down the dimensions of each physical quantity: [F] = MLT^-2, [m] = M, [a] = LT^-2.
3. Substitute the dimensions into the equation: [MLT^-2] = [M][LT^-2].
4. Simplify the equation: [MLT^-2] = [MLT^-2].
5. Check that the dimensions on both sides of the equation are equal. Since they are, the equation is dimensionally balanced and therefore correct.
Importance of Dimensional Balance:
Dimensional balance is important because it ensures that an equation is physically meaningful. If an equation is not dimensionally balanced, it means that the units of measurement on one side of the equation do not match the units of measurement on the other side of the equation. This can lead to nonsensical or physically impossible results. By using dimensional analysis to check the dimensional balance of an equation, we can ensure that the equation is physically meaningful and can be used to make accurate predictions about the behavior of physical systems.
Community Answer
what is dimensional balance of an equation how can we check the correc...
By checking dimensional formulas of LHS and RHS
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
what is dimensional balance of an equation how can we check the correctness of an equation by this
Question Description
what is dimensional balance of an equation how can we check the correctness of an equation by this for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about what is dimensional balance of an equation how can we check the correctness of an equation by this covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for what is dimensional balance of an equation how can we check the correctness of an equation by this.
what is dimensional balance of an equation how can we check the correctness of an equation by this for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about what is dimensional balance of an equation how can we check the correctness of an equation by this covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for what is dimensional balance of an equation how can we check the correctness of an equation by this.
Solutions for what is dimensional balance of an equation how can we check the correctness of an equation by this in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of what is dimensional balance of an equation how can we check the correctness of an equation by this defined & explained in the simplest way possible. Besides giving the explanation of
what is dimensional balance of an equation how can we check the correctness of an equation by this, a detailed solution for what is dimensional balance of an equation how can we check the correctness of an equation by this has been provided alongside types of what is dimensional balance of an equation how can we check the correctness of an equation by this theory, EduRev gives you an
ample number of questions to practice what is dimensional balance of an equation how can we check the correctness of an equation by this tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup